Recently it has been shown in 0901.0931 [hep-th] that the approach to extremality for the non-extremal Reissner-Nordstrom black hole is not continuous. The non-extremal RN black hole splits into two spacetimes at the extremality: an extremal black hole and a disconnected $AdS_2\\times S^2$ space which has been called the \"compactification solution\". As a possible resolution for understanding the entropy of extremal RN black hole, it has been speculated that the entropy of the non-extremal black hole may be carried by the latter solution. By uplifting the four dimensional \"compactification solution\" with electric charge $Q_e$ to a five dimensional solution, we show that this solution is dual to a CFT with central charge $c=6Q_e^3$. The Cardy formula then shows that the microscopic entropy of the CFT is the same as the macroscopic entropy of the \"compactification solution\".

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